Git before 2.19.2 on Linux and UNIX executes commands from the current working directory (as if '.' were at the end of $PATH) in certain cases involving the run_command() API and run-command.c, because there was a dangerous change from execvp to execv during 2017.
GIT version 2.15.1 and earlier contains a Input Validation Error vulnerability in Client that can result in problems including messing up terminal configuration to RCE. This attack appear to be exploitable via The user must interact with a malicious git server, (or have their traffic modified in a MITM attack).
Git through 2.14.2 mishandles layers of tree objects, which allows remote attackers to cause a denial of service (memory consumption) via a crafted repository, aka a Git bomb. This can also have an impact of disk consumption; however, an affected process typically would not survive its attempt to build the data structure in memory before writing to disk.